Standard transparency:
Anything black on your textures will be hidden when you use transparency mode 1.
Specified transparency:
Like above, and using transparency mode 1, except you would set the transparency colour, say RGB(255,0,255) which is a loud pinky-purple colour that most people would never use. This is a good way to get black into your media, I prefer to use this for strickly 2D stuff that does'nt need Anti-Aliasing. You would set the new default transparency colour using SET IMAGE COLOURKEY.
Alpha transparency:
The best format for this is .PNG, and a decent art package like Photoshop CS or PSP9. It uses the art packages transparency to set the transparent areas using transparency mode 2 or 3. This gives full control over everything, lets you have translucent but coloured glass and AA and cool stuff like that. It's more time consuming but gives much better results.
1-Bit Alpha transparency:
This takes your alpha layer in the same way as above, except that the alpha is set to a binary state, which makes it possible to make smooth solid curves instead of blends, nice for leaves and suchlike - a lot like the early MOH games. This gives the impression that the texture is much higher resolution, because of the way the alpha is calculated - the texture still affects the polygon, but where the alpha drops below a certain point the texture is ignored, and because the alpha is smooth, you get curves and sharp edges that defy normal transparencies resolution. This is a good mode for any solid texture that you want to cut holes in, especiall nice round holes - consider this anyone who wants incredibly low polygon cars - you can use alpha to cut out all the fidly bits like the wheel recesses and windows. You'd use transparency mode 4 for this.
Van-B

Put away, those fiery biscuits!